Lesson Plan/Solving Equations Student: Jarloth wolo Cooperating Teacher’s Approval: Date: 10-6-10 Subject: Functions and Algebra Topic: _Solving Equations Grade: 9th Grade Allocated Time: 45 mins. Student Population: _There are twenty-six students in the 9th grade class comprising of 15 male students and 11 female students. The class is diverse ethnically with a fairly even mix of Caucasian, Black, and Hispanic Students. Two students are Special Education students but can fairly function on their own. State Standards: Specific Number: 2.8.11.D Exact wording: Formulate expressions,equations,inequalities,systems of equations.system of inequalities and matrices to model routine and non-routine problem situations. : 2.8.8.E : Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy.
Goal for Understanding: _Students will demonstrate the ability to interpret and communicate solutions to mathematically and real world situation.
Instructional Objective (Statement):
Student Behaviors Students will solve linear equations in order to interpret real-world situations.
Sources of Evidence • Students will write equations of real-world situations.
• Students will solve a one variable equation for the unknown.
• Students will graph equations
• Students will interpret solution in light of the context of a problem.
• Student will evaluate an equation for a given value.
Criteria for Evaluation Worksheets and Rubric
Teaching to the Objective
Estimated Time:5 mins. 37mins. 3mins.
Teaching to the Objective Introduction/Motivation/ Prior Knowledge : Students will be given an incomplete table of x and y values and will be asked to complete the table and determine the function rule based on the pattern observed. Students will also be asked to find a y value given some value of x in the future. Developmental Activities: An equation is a mathematical sentence that has two expressions separated by an equal sign. The expression on the left side has the same value as the expression of the right side. An expression is also a mathematical sentence but differs from an equation because it does not have an equal sign. A linear equation is any equation that involves constants and variables that are multiplied by coefficient. The variable has a degree of one. A linear equation when graphed produces a straight line. Hence a linear ( line ) equation. There are three forms of a linear equation. 1. General form: AX + BY = C 2. Point – slope form: y-yi = m(x-xi) 3. Slope – intercept form : y= mx + b The slope intercept form is the most widely used form and hence will be used in this lesson. Teacher will explain or describe an equation of the form, y = mx + b. y = the dependent variable x = the independent variable m= the slope ( in terms of graph, it shows the” slantness” of the line. It is the unit item,ie, the cost per item. b = the y-intercept, it’s the y-coordinate of the point where the line crosses the y-axis. It is the initial cost or basic fee or the value of y when x= 0. The following example will be modeled for the students: In order to become a member of A & A CD Club, a member must pay $50 and purchase each CD for $10. ( a) Write and equation relating the Total cost (y) to the number of CD’s Purchased ( x ). (b) How much will it cost a member if he/she purchases 6 cd’s ? (c) Interpret the y-intercept in the context of the problem. (d) If a member has $120, how many cd’s can he/she purchase? Answer: Let x = the number of cds purchased and y= the Total cost. (a) The total cost is equal to the cost per cd times the number of cds plus the initial fee. y = mx + b y= 10x + 50 (b) Substitute for the number of cds purchased, x = 6, y= 10• 6 + 50 y = 60 + 50, y= 110. ( c ) the y-intercept is the fee a member pays for becoming a member. It the fee a member pays even if no cds were purchased. ( d) Substitute for y ( the total cost) y = 120 y = 10x + 50 120 = 10x + 50 Subtract 50 from both sides of the equation 120 ̶ 50 = 10x + 50 ̶ 50 70 = 10x Divide both sides of the equation by 10 70 ÷ 10 = 10x ÷ 10 7 = x, which 7 cds. Assessment: ( See assessment sheet attached ) Closure: What does the " m " in the equation y = mx + b mean?
Differentiation: An inclusion activity will be to have students give the x-values a red color and the y-values a yellow color
A balanced scale will be drawn on the black board and explanation be given to relate an equation to a balanced scale. Every on left side must be equal to everything on the right side
An inclusion activity will be to have students use specific colors for each of the explained variables.
Follow-up: In the equation y = 3x + 2, given x = 9, find the y value.
Materials: Worksheets, Rubric, Calculators,
References: Algebra I Textbook: Holt ,Rinehart, and Winston (2004); Algebra I Textbook: Algebra I Textbook: Prentice Hall Mathematics (2004).
Technology: Overhead projector use, Calculator usage.
Assessment 1. James is a high school student who types research papers for college students during the summer. He charges $2 per page plus &50. •Write an equation relating the total amount(y) that James will receive for typing x number of pages. • What is the y-intercept of your equation ? What does the y-intercept mean in the Context of this problem? • James needs $600 to buy a laptop. What is the maximum number of pages James needs to type? Use mathematics to explain your answer. Use words, symbols, or both in your explanation.
ASSESSMENT RUBRIC
Score of 1 : The response shows an inaccurate application of a reasonable strategy for
solving then problem. No contextual meaning is provided and no
explanation is given. The equation is correct. Some conceptual
understanding and analysis of the problem.
Score of 2 : The response show an incomplete application of a reasonable strategy.
Contextual meaning is incomplete. Equation is correct and answer is correct
but no explanation is given. Some conceptual understanding and analysis of
the problem.
Score of 3: The response shows an application of a reasonable strategy for solving the
problem. Instead of providing contextual meaning, descriptions of some key
concepts are provided. Equation is correct. Answer is correct with very little
explanation. Clear understanding and analysis of the problem.
Score of 4: The response shows an application of a reasonable strategy that provided the
correct solution within the context of the problem. The equation and answer
are correct, and clear explanation is provided. Complete understanding and
analysis of the problem.
Student: Jarloth wolo Cooperating Teacher’s Approval: Date: 10-6-10
Subject: Functions and Algebra Topic: _Solving Equations Grade: 9th Grade
Allocated Time: 45 mins.
Student Population: _There are twenty-six students in the 9th grade class comprising of 15 male students and 11 female students. The class is diverse ethnically with a fairly even mix of Caucasian, Black, and Hispanic Students. Two students are Special Education students but can fairly function on their own.
State Standards:
Specific Number: 2.8.11.D Exact wording: Formulate expressions,equations,inequalities,systems of equations.system of inequalities and matrices to model routine and non-routine problem situations.
: 2.8.8.E : Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy.
Goal for Understanding: _Students will demonstrate the ability to interpret and communicate solutions to mathematically and real world situation.
Instructional Objective (Statement):
• Students will solve a one variable equation for the unknown.
• Students will graph equations
• Students will interpret solution in light of the context of a problem.
• Student will evaluate an equation for a given value.
Teaching to the Objective
37mins.
3mins.
Introduction/Motivation/
Prior Knowledge : Students will be given an incomplete table of x and y values and will be asked to complete the table and determine the function rule based on the pattern observed. Students will also be asked to find a y value given some value of x in the future.
Developmental Activities: An equation is a mathematical sentence that has two expressions separated by an equal sign. The expression on the left side has the same value as the expression of the right side. An expression is also a mathematical sentence but differs from an equation because it does not have an equal sign.
A linear equation is any equation that involves constants and variables that are multiplied by coefficient. The variable has a degree of one. A linear equation when graphed produces a straight line. Hence a linear ( line ) equation.
There are three forms of a linear equation.
1. General form: AX + BY = C
2. Point – slope form: y-yi = m(x-xi)
3. Slope – intercept form : y= mx + b
The slope intercept form is the most widely used form and hence will be used in this lesson.
Teacher will explain or describe an equation of the form, y = mx + b.
y = the dependent variable
x = the independent variable
m= the slope ( in terms of graph, it shows the” slantness” of the line. It is the unit item,ie, the cost per item.
b = the y-intercept, it’s the y-coordinate of the point where the line crosses the y-axis. It is the initial cost or basic fee or the value of y when x= 0.
The following example will be modeled for the students:
In order to become a member of A & A CD Club, a member must pay $50 and purchase each CD for $10.
( a) Write and equation relating the Total cost (y) to the number of CD’s Purchased ( x ).
(b) How much will it cost a member if he/she purchases 6 cd’s ?
(c) Interpret the y-intercept in the context of the problem.
(d) If a member has $120, how many cd’s can he/she purchase?
Answer: Let x = the number of cds purchased and y= the Total cost.
(a) The total cost is equal to the cost per cd times the number of cds plus the initial fee.
y = mx + b
y= 10x + 50
(b) Substitute for the number of cds purchased, x = 6, y= 10• 6 + 50
y = 60 + 50, y= 110.
( c ) the y-intercept is the fee a member pays for becoming a member. It the fee a member pays even if no cds were purchased.
( d) Substitute for y ( the total cost) y = 120
y = 10x + 50
120 = 10x + 50
Subtract 50 from both sides of the equation
120 ̶ 50 = 10x + 50 ̶ 50
70 = 10x
Divide both sides of the equation by 10
70 ÷ 10 = 10x ÷ 10
7 = x, which 7 cds.
Assessment: ( See assessment sheet attached )
Closure: What does the " m " in the equation y = mx + b mean?
A balanced scale will be drawn on the black board and explanation be given to relate an equation to a balanced scale. Every on left side must be equal to everything on the right side
An inclusion activity will be to have students use specific colors for each of the explained variables.
Follow-up: In the equation y = 3x + 2, given x = 9, find the y value.
Materials: Worksheets, Rubric, Calculators,
References: Algebra I Textbook: Holt ,Rinehart, and Winston (2004); Algebra I Textbook: Algebra I Textbook: Prentice Hall Mathematics (2004).
Technology: Overhead projector use, Calculator usage.
Assessment
1. James is a high school student who types research papers for college students during the summer. He charges $2 per page plus &50.
•Write an equation relating the total amount(y) that James will receive for typing x
number of pages.
• What is the y-intercept of your equation ? What does the y-intercept mean in the
Context of this problem?
• James needs $600 to buy a laptop. What is the maximum number of pages
James needs to type? Use mathematics to explain your answer. Use words,
symbols, or both in your explanation.
ASSESSMENT RUBRIC
Score of 1 : The response shows an inaccurate application of a reasonable strategy for
solving then problem. No contextual meaning is provided and no
explanation is given. The equation is correct. Some conceptual
understanding and analysis of the problem.
Score of 2 : The response show an incomplete application of a reasonable strategy.
Contextual meaning is incomplete. Equation is correct and answer is correct
but no explanation is given. Some conceptual understanding and analysis of
the problem.
Score of 3: The response shows an application of a reasonable strategy for solving the
problem. Instead of providing contextual meaning, descriptions of some key
concepts are provided. Equation is correct. Answer is correct with very little
explanation. Clear understanding and analysis of the problem.
Score of 4: The response shows an application of a reasonable strategy that provided the
correct solution within the context of the problem. The equation and answer
are correct, and clear explanation is provided. Complete understanding and
analysis of the problem.
A: 4
B: 3
C: 2
D: 1